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A087648
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a(n) = (1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)).
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7
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1, 3, 9, 31, 120, 514, 2407, 12205, 66491, 386699, 2388096, 15589732, 107165081, 773106715, 5836100685, 45981026703, 377230766908, 3215977070706, 28437411817135, 260380616093533, 2464930698184351, 24091925888687459, 242802079705721156, 2520198597834860148
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OFFSET
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0,2
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COMMENTS
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Sum of last number in all set partitions of n+1. E.g. The set partitions of 3 are {1,1,1}, {1,1,2}, {1,2,1}, {1,2,2} and {1,2,3}, so a(2) = 1+2+1+2+3 = 9. - Franklin T. Adams-Watters, Jun 07 2006
Number of partitions of the (n+2)-multiset {0,0,1,2,...,n} into distinct multisets. Also number of factorizations of 2 * Product_{i=1..n+1} prime(i) into distinct factors. - Alois P. Heinz, Jul 30 2021
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LINKS
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MATHEMATICA
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f[0]=1; f[n_] := Sum[ StirlingS2[n, k]*Binomial[k+2, k ], {k, 1, n}]; Table[ f[n], {n, 0, 20}] (* Zerinvary Lajos, Mar 31 2007 *)
(#[[3]]+#[[2]]-#[[1]])/2&/@Partition[BellB[Range[0, 30]], 3, 1] (* Harvey P. Dale, Jul 20 2021 *)
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PROG
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(Magma) [(1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)) : n in [0..30]]; // Vincenzo Librandi, Nov 13 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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